This paper is concerned about the definition of a first-order method for the solution of l0- penalized problems with simple constraints. We propose a reduced dimension Frank-Wolfe algorithm and show that the subproblem related with computation of the FW direction can be solved analitically at least for some sets of simple constraints. The proposed method is applied to the numerical solution of two practical optimization problems, namely, the sparse principal component analysis and the sparse reconstruction of noisy signals. In both cases, the reported numerical performances and comparisons with state-of-the-art solvers show efficiency of the proposed method.
A first-order method for l0-penalized problems with simple constraints
G Liuzzi;
2012
Abstract
This paper is concerned about the definition of a first-order method for the solution of l0- penalized problems with simple constraints. We propose a reduced dimension Frank-Wolfe algorithm and show that the subproblem related with computation of the FW direction can be solved analitically at least for some sets of simple constraints. The proposed method is applied to the numerical solution of two practical optimization problems, namely, the sparse principal component analysis and the sparse reconstruction of noisy signals. In both cases, the reported numerical performances and comparisons with state-of-the-art solvers show efficiency of the proposed method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.